Details

sample30.0ms

Algorithm

intervals

Results

15.0ms	256×	body	80	valid
7.0ms	256×	pre	80	true

simplify1.9s

Counts: 1 → 1

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 8.8b

localize12.0ms

Local error

Found 2 expressions with local error:

8.8b	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
0.4b	(* (/ b a) (/ b a))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
40×	`times-frac`
31×	`*-un-lft-identity` `add-cube-cbrt`
14×	`add-cbrt-cube` `add-exp-log`
13×	`swap-sqr` `associate-r` `associate-l`
10×	`pow1`
4×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
3×	`sqrt-prod`
2×	`insert-posit16` `add-log-exp`
1×	`pow2` `frac-times` `rem-sqrt-square` `sqrt-pow1` `pow-plus` `pow1/2` `pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up`

Counts

2 → 82

Calls

2 calls:

Slowest

12.0ms	(* (/ b a) (/ b a))
1.0ms	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

series80.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

57.0ms	(* (/ b a) (/ b a))
22.0ms	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

simplify1.6s

Counts: 88 → 88

prune799.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 8.8b

localize28.0ms

Local error

Found 3 expressions with local error:

8.8b	(sqrt (fabs (- 1 (/ (* (/ b a) b) a))))
6.6b	(/ (* (/ b a) b) a)
0.2b	(* (/ b a) b)

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
17×	`add-cbrt-cube` `add-exp-log`
14×	`*-un-lft-identity` `add-cube-cbrt`
13×	`times-frac` `associate-l`
6×	`pow1`
5×	`cbrt-undiv` `div-exp`
4×	`prod-exp` `cbrt-unprod`
3×	`associate-/r` `associate-r*` `sqrt-prod` `insert-posit16` `add-log-exp`
2×	`associate-*l/` `div-inv` `unswap-sqr`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `-commutative` `associate-/l` `associate-/l/`

Counts

3 → 72

Calls

3 calls:

Slowest

22.0ms	(/ (* (/ b a) b) a)
17.0ms	(* (/ b a) b)
2.0ms	(sqrt (fabs (- 1 (/ (* (/ b a) b) a))))

series68.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

34.0ms	(/ (* (/ b a) b) a)
21.0ms	(* (/ b a) b)
13.0ms	(sqrt (fabs (- 1 (/ (* (/ b a) b) a))))

simplify1.8s

Counts: 81 → 81

prune841.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 8.6b

localize26.0ms

Local error

Found 4 expressions with local error:

16.2b	(cbrt (* (sqrt (fabs (- 1 (* (/ b a) (/ b a))))) (fabs (- 1 (* (/ b a) (/ b a))))))
8.8b	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
0.4b	(* (/ b a) (/ b a))
0.4b	(* (/ b a) (/ b a))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

87×	`add-sqr-sqrt`
80×	`times-frac`
61×	`*-un-lft-identity` `add-cube-cbrt`
28×	`add-cbrt-cube` `add-exp-log`
26×	`swap-sqr` `associate-r` `associate-l`
19×	`pow1`
8×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
4×	`insert-posit16` `add-log-exp`
3×	`sqrt-prod`
2×	`pow2` `frac-times` `pow-plus` `pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up`
1×	`cbrt-prod` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow1/3` `cube-unmult` `rem-cbrt-cube`

Counts

4 → 161

Calls

4 calls:

Slowest

24.0ms	(* (/ b a) (/ b a))
18.0ms	(* (/ b a) (/ b a))
4.0ms	(cbrt (* (sqrt (fabs (- 1 (* (/ b a) (/ b a))))) (fabs (- 1 (* (/ b a) (/ b a))))))
1.0ms	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

series115.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

42.0ms	(* (/ b a) (/ b a))
29.0ms	(* (/ b a) (/ b a))
23.0ms	(cbrt (* (sqrt (fabs (- 1 (* (/ b a) (/ b a))))) (fabs (- 1 (* (/ b a) (/ b a))))))
22.0ms	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

simplify1.2s

Counts: 173 → 173

prune2.1s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 8.6b

localize36.0ms

Local error

Found 4 expressions with local error:

45.7b	(posit16->real (real->posit16 (* (/ b a) b)))
8.8b	(sqrt (fabs (- 1 (/ (posit16->real (real->posit16 (* (/ b a) b))) a))))
6.6b	(/ (posit16->real (real->posit16 (* (/ b a) b))) a)
0.2b	(* (/ b a) b)

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
21×	`*-un-lft-identity` `add-cube-cbrt`
19×	`times-frac`
13×	`associate-l`
11×	`add-cbrt-cube` `add-exp-log`
7×	`pow1`
4×	`insert-posit16` `add-log-exp`
3×	`associate-/r` `associate-r` `sqrt-prod` `associate-/l`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `associate-l/` `-commutative` `remove-posit16`

Counts

4 → 84

Calls

4 calls:

Slowest

9.0ms	(* (/ b a) b)
4.0ms	(/ (posit16->real (real->posit16 (* (/ b a) b))) a)
1.0ms	(sqrt (fabs (- 1 (/ (posit16->real (real->posit16 (* (/ b a) b))) a))))
0.0ms	(posit16->real (real->posit16 (* (/ b a) b)))

series122.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

40.0ms	(/ (posit16->real (real->posit16 (* (/ b a) b))) a)
36.0ms	(posit16->real (real->posit16 (* (/ b a) b)))
34.0ms	(* (/ b a) b)
13.0ms	(sqrt (fabs (- 1 (/ (posit16->real (real->posit16 (* (/ b a) b))) a))))

simplify998.0ms

Counts: 96 → 96

prune1.8s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 8.6b

regimes158.0ms

Accuracy

0% (0.1b remaining)

Error of 7.6b against oracle of 7.5b and baseline of 7.6b

bsearch2.0ms

end0.0ms

sample1.3s

Algorithm

intervals

Results

834.0ms	8000×	body	80	valid
352.0ms	8000×	pre	80	true